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Category > Calculus Posted 22 Apr 2017 My Price 2.00

Find the derivative of x^(3/2) using the definition of a derivative.

Find the derivative of x^(3/2) using the definition of a derivative.

You cannot use the power rule or any other differentiation rules.

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Alpha Geek
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Status NEW Posted 22 Apr 2017 09:04 AM My Price 2.00

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file 1492852598-Find the derivative.docx preview (98 words )
[----------- f(-----------x+h-----------) ------------ f(-----------x) -----------/ h----------- ] -----------= [----------- (x-----------+h)-----------^3 ------------ x-----------^3 -----------] /----------- hU-----------se -----------the----------- bi-----------nom-----------ial----------- th-----------eor-----------em -----------to -----------exp-----------and----------- th-----------e n-----------ume-----------rat-----------or -----------:[f-----------(x+-----------h) ------------ f-----------(x)----------- / -----------h] -----------= [----------- (x-----------^3 -----------+ 3-----------x^2-----------h +----------- 3x-----------h^2----------- + -----------h^3-----------) ------------ x^-----------3 ]----------- / -----------h= -----------[ 3-----------x^2-----------h +----------- 3x-----------h^2----------- + -----------h^3----------- ] -----------/ h-----------Can-----------cel----------- ou-----------t t-----------he -----------h f-----------rom----------- nu-----------mer-----------ato-----------r a-----------nd -----------den-----------omi-----------nat-----------or -----------:= -----------[ 3-----------x^2----------- + -----------3xh----------- + -----------h^2----------- ]N-----------ow -----------tak-----------e t-----------he -----------lim-----------it -----------as -----------h -------------&a-----------mp;-----------gt;----------- 0 -----------to -----------get-----------3x^-----------2 /----------- [ -----------2 *----------- x^-----------(3/-----------2) -----------]= -----------(3/-----------2) -----------* x-----------^2 -----------* x-----------^( ------------ 3-----------/2 -----------)= -----------(3/-----------2) -----------* x-----------^(1-----------/2)-----------. -----------Hen-----------ce,----------- th-----------e d-----------eri-----------vat-----------ive----------- of----------- x^-----------(3/-----------2) -----------is(-----------3/2-----------) *----------- x^-----------(1/-----------2).----------- -----------
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